Inclusive and multiplicity-dependent pseudorapidity densities of charged particles in pp collisions at $\mathbf{\sqrt{s} = 13.6}$ TeV

This paper presents the first measurements of inclusive and multiplicity-dependent pseudorapidity densities of charged particles in proton-proton collisions at the record center-of-mass energy of $\sqrt{s} = 13.6$ TeV, revealing that particle production in high-multiplicity events follows a power-law scaling with energy and establishing a new reference for LHC physics.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful "smash-up" machine. Scientists fire two tiny protons (the building blocks of atoms) at each other at nearly the speed of light. When they collide, they don't just bounce off; they shatter, creating a chaotic explosion of new particles.

This paper is a detailed report card from the ALICE experiment, one of the detectors watching these collisions. It focuses on a specific, record-breaking event: smashing protons together at an energy level of 13.6 TeV. This is the highest energy ever achieved in a proton-proton collision, essentially the "supercharged" version of previous experiments.

Here is the breakdown of what they found, using some everyday analogies:

1. The Goal: Counting the Debris

When two cars crash, you get a pile of twisted metal, glass, and plastic. In particle physics, when protons crash, they create a shower of charged particles (mostly pions, which are like the "glass shards" of the subatomic world).

The scientists wanted to answer two main questions:

• The "Average" Crash: On average, how many of these "shards" fly out in the middle of the explosion?
• The "Busy" vs. "Quiet" Crash: Does the number of shards change if the crash is a tiny fender-bender or a massive, total-destroying wreck?

2. The New Tools: A Better Camera

To take this picture, ALICE upgraded its "camera" (the detector) during a long shutdown.

• The Old Way: Previous cameras took snapshots. If two crashes happened at the exact same time, the photo got blurry.
• The New Way: The new camera is like a high-speed video camera that never stops recording. It can see every single particle passing through, even if thousands of crashes are happening in rapid succession. This allowed them to collect a dataset 300 times larger than before, giving them a much clearer picture.

3. The Main Findings

A. The Average Explosion (The "Midpoint" Count)

The scientists counted how many particles appeared right in the center of the collision (called "midrapidity").

• The Result: They found an average of 7.1 particles per unit of area.
• The Trend: They compared this to crashes at lower energies (like 900 GeV or 13 TeV). They found that as you turn up the "volume" (energy) of the crash, the number of particles doesn't just go up linearly; it follows a specific mathematical curve (a power law). It's like turning up a radio: the volume gets louder, but the relationship between the knob position and the sound follows a predictable pattern. This new 13.6 TeV data point fits perfectly into that pattern, confirming our understanding of how energy turns into matter.

B. The "Busy" vs. "Quiet" Crashes (Multiplicity)

Not all crashes are the same. Some are gentle (low multiplicity), and some are violent (high multiplicity).

• The Analogy: Imagine a party.
  • Low Multiplicity: A quiet dinner party where only a few people are talking.
  • High Multiplicity: A massive rock concert where the crowd is dense and everyone is shouting.
• The Discovery: The scientists looked at the "rock concert" crashes (the top 1% of the busiest events). They found that in these high-energy, high-activity crashes, the density of particles in the center was five times higher than in the quiet crashes.
• The Surprise: This is important because in the past, we thought small collisions (like proton-proton) were too simple to create the "soup" of matter seen in giant nuclear collisions (like gold-gold). But these high-multiplicity proton crashes are showing signs of behaving like those giant, complex collisions. It suggests that even in a small "party," if enough people show up, the dynamics change.

4. The Computer Models: Do They Get It Right?

Scientists use super-computers to simulate these crashes before they happen. Two famous "simulators" are PYTHIA and EPOS.

• PYTHIA: This model is like a very good weather forecaster. It predicted the shape of the particle distribution almost perfectly. It knew exactly how the "debris" would spread out.
• EPOS: This model is a bit more optimistic. It predicted there would be more particles in the center than actually appeared (overestimating by about 6%).
• The Takeaway: The models get the general idea right, but they struggle with the extremes. They overestimate the chaos in the biggest crashes and underestimate the quiet ones. This tells the model-makers: "You need to tweak your settings on how particles interact when things get really crowded."

5. Why Does This Matter?

You might ask, "Why do we care about counting subatomic glass shards?"

1. The Rules of the Universe: These collisions test the Standard Model of physics. If the numbers didn't fit the power-law pattern, it would mean our understanding of how the universe works is broken. They fit, so our physics is solid.
2. The "Little Big Bang": The high-multiplicity crashes are the closest we can get to recreating the conditions of the Quark-Gluon Plasma—a state of matter that existed microseconds after the Big Bang. By studying how these particles behave in crowded proton crashes, we learn how the early universe cooled down and formed matter.
3. Tuning the Engines: Just as a mechanic tunes a car engine to run smoother, physicists use these results to "tune" their computer models. This makes future predictions more accurate, helping us design better experiments and understand the fundamental forces of nature.

Summary

In short, the ALICE team smashed protons together harder than ever before. They used a super-fast camera to count the resulting particles. They found that the number of particles grows predictably with energy, and that the "busiest" crashes look surprisingly complex, hinting at deep connections between small and large particle collisions. Their data is now the new gold standard for anyone trying to simulate the subatomic world.

Technical Summary

1. Problem and Motivation

The primary goal of this study is to characterize the production of primary charged particles in proton-proton (pp) collisions at the highest center-of-mass energy achieved at the Large Hadron Collider (LHC) to date: $\sqrt{s} = 13.6$ TeV.

• Scientific Context: Understanding the multiplicity of primary charged particles ($dN_{ch}/d\eta$) is crucial for probing the interplay between soft and hard partonic scattering processes in Quantum Chromodynamics (QCD).
• The Gap: While previous measurements existed up to 13 TeV, the transition to 13.6 TeV (LHC Run 3) offers a new energy frontier. Furthermore, existing models (event generators) struggle to simultaneously describe inclusive particle production and the specific features observed in high-multiplicity events (e.g., ridge structures, strangeness enhancement), which may hint at collective effects or Quark-Gluon Plasma (QGP)-like behavior in small systems.
• Specific Challenge: The paper addresses the need for precise, multiplicity-differential measurements to constrain models of Multiple-Parton Interactions (MPI), color reconnection (CR), and hadronization mechanisms, which are critical for tuning Monte Carlo event generators like PYTHIA and EPOS.

2. Methodology and Experimental Setup

Data Sample and Event Selection:

• Dataset: The analysis utilizes a subset of the 2022 LHC Run 3 data, comprising approximately 3 billion minimum-bias (MB) events.
• Event Class: Results are reported for the INEL>0 event class, defined as inelastic events containing at least one charged particle in the pseudorapidity range $|\eta| < 1$. This selection suppresses diffractive contributions, avoiding the need for model-dependent corrections for diffractive cross-sections.
• Multiplicity Classification: Event activity is classified using the FT0M forward multiplicity estimator (sum of amplitudes from FT0A and FT0C detectors covering $3.5 < \eta < 4.9$ and $-3.3 < \eta < -2.1$). Multiplicity classes are defined by percentiles of the visible cross-section, ranging from the highest multiplicity (0–1%) to the lowest (70–100%).

Detector and Reconstruction:

• Upgrades: The analysis leverages the ALICE detector upgrades from the Long Shutdown 2 (2019–2022), specifically the Inner Tracking System (ITS) with seven layers of Monolithic Active Pixel Sensors (MAPS) and the Time Projection Chamber (TPC) equipped with Gas Electron Multiplier (GEM) foils for continuous readout.
• Tracking: Tracks are reconstructed in the range $|\eta| < 1.5$. The analysis uses global tracks (combining ITS and TPC hits) and ITS-only tracks (for high $p_T$ or specific geometrical acceptance). TPC-only tracks are excluded due to poor vertex association.
• Corrections: Raw distributions are corrected for:
  1. Track-to-particle efficiency: Accounting for detector inefficiencies and secondary particles.
  2. Vertex reconstruction efficiency: For events where the primary vertex was not reconstructed.
  3. Selection bias: Correcting for the INEL>0 requirement.
  4. Strangeness content: A scaling factor is applied to Monte Carlo (MC) simulations to match the observed abundance of strange hadrons ($K^0_S, \Lambda, \bar{\Lambda}$), as previous MC versions underestimated strangeness.

Systematic Uncertainties:
Key sources include azimuthal acceptance, vertex position ($z_{vtx}$), low-$p_T$ extrapolation, strangeness content, particle composition, material budget, and track selection criteria. The total systematic uncertainty ranges from 1.4% to 2.5% depending on the multiplicity class.

3. Key Contributions

1. First Measurement at 13.6 TeV: This is the inaugural measurement of charged-particle pseudorapidity density at the new LHC energy of 13.6 TeV.
2. Multiplicty-Dependent Analysis: Unlike previous inclusive-only studies, this paper provides a granular breakdown of $dN_{ch}/d\eta$ across 10 distinct multiplicity percentiles (0–1% to 70–100%), offering a stringent test for MPI models.
3. Model Benchmarking: The results provide a critical benchmark for PYTHIA 8 (Monash 2013 tune and Color Reconnection variations) and EPOS4 (including Parameterised Fluid Expansion), specifically testing their ability to reproduce high-multiplicity phenomena in small collision systems.
4. Energy Scaling Validation: The study extends the power-law scaling analysis of particle production to the highest available energy, confirming the continuity of QCD scaling behaviors.

4. Results

Inclusive Results:

• The average charged-particle pseudorapidity density at midrapidity ($|\eta| < 0.5$) for INEL>0 events is measured to be:
  $$\langle dN_{ch}/d\eta \rangle = 7.10 \pm 0.18$$
• Energy Scaling: When combined with lower-energy data (from ISR to 13 TeV), the results follow a power-law scaling $\langle dN_{ch}/d\eta \rangle \propto s^\delta$. The extracted exponent for INEL>0 events is $\delta = 0.115 \pm 0.003$. The new 13.6 TeV data point is consistent with this trend.

Model Comparison (Inclusive):

• PYTHIA 8 Monash 2013: Provides an excellent description of the data across the entire pseudorapidity range, agreeing within 1%.
• EPOS4: Overestimates the data by approximately 6% at midrapidity ($\eta=0$) and shows increasing discrepancies in the forward region.
• Color Reconnection (CR): Variations in PYTHIA 8 (CR1, CR2) show different normalizations (CR1 overestimates by ~4%, CR2 underestimates by ~3%) but maintain the correct shape.

Multiplicity-Dependent Results:

• Trend: There is a strong correlation between forward event activity and midrapidity particle density. The highest multiplicity class (0–1%) exhibits a density of $\approx 21.8$, roughly 5 times higher than the lowest class (70–100%, $\approx 3.7$).
• Model Performance vs. Multiplicity:
  • High Multiplicity (0–1%): Both EPOS4 and PYTHIA 8 overestimate the data. EPOS4 significantly overestimates the yield, while PYTHIA 8 overestimates by a smaller margin.
  • Intermediate Multiplicity (10–30%): All models show their best agreement with data in this region.
  • Low Multiplicity (70–100%): All models underestimate the data by up to 40%.
• Comparison with Run 2: The study notes that multiplicity classes defined by the new FT0M estimator (Run 3) select events with different midrapidity densities compared to the V0M estimator (Run 2), highlighting the importance of consistent multiplicity definitions for model tuning.

5. Significance and Conclusions

• QCD Phenomenology: The confirmation of power-law scaling up to 13.6 TeV reinforces the understanding of particle production mechanisms across a vast energy range.
• Event Generator Tuning: The discrepancies observed, particularly the underestimation of low-multiplicity events and overestimation of high-multiplicity events by current models, indicate that MPI modeling, color reconnection mechanisms, and hadronization processes require further refinement.
• Small System Dynamics: The results provide essential constraints for understanding whether collective effects (like flow) in high-multiplicity pp collisions are driven by MPI density or other mechanisms. The failure of current models to quantitatively reproduce the full multiplicity dependence suggests that the transition from soft to hard processes and the role of color reconnection are not yet fully understood.
• Future Reference: This dataset serves as a new standard reference for charged-particle production at the LHC, guiding future theoretical developments and experimental analyses in Run 3 and beyond.